Comparing Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does the rate of change represent in a function?

Back

The rate of change represents how much the output value of a function changes for a given change in the input value.

Front

How do you determine the rate of change from a table of values?

Back

The rate of change can be determined by calculating the difference in output values divided by the difference in input values between two points.

Front

What is the initial value of a function?

Back

The initial value is the output of the function when the input is zero, often represented as the y-intercept in a graph.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

How do you write an equation from a table of values?

Back

To write an equation from a table, identify the rate of change and the initial value, then use the slope-intercept form y = mx + b.

Front

What is the difference between a linear function and a non-linear function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a non-linear function has a variable rate of change and graphs as a curve.

Front

What does it mean for two functions to be equivalent?

Back

Two functions are equivalent if they produce the same output for every input in their domain.

Front

How can you compare the starting values of two functions?

Back

You can compare the starting values by evaluating each function at x = 0 and determining which output is greater.

Front

What is a set-up fee in a function context?

Back

A set-up fee is a fixed cost that is added to the variable costs in a function, often representing an initial charge before usage.